code: def test_generate_gate_rules_2():
      # Test with Muls
      (x, y, z, h) = create_gate_sequence()
      ph = PhaseGate(0)
      cgate_t = CGate(0, TGate(1))
  
      # Note: 1 (type int) is not the same as 1 (type One)
      expected = {(x, Integer(1))}
      assert generate_gate_rules((x,), return_as_muls=True) == expected
  
      expected = {(Integer(1), Integer(1))}
      assert generate_gate_rules(x * x, return_as_muls=True) == expected
  
      expected = {((), ())}
      assert (
          generate_gate_rules(x * x, return_as_muls=False) == expected
      )
  
      gate_rules = {
          (x * y * x, Integer(1)),
          (y, Integer(1)),
          (y * x, x),
          (x * y, x),
      }
      assert (
          generate_gate_rules(x * y * x, return_as_muls=True)
          == gate_rules
      )
  
      gate_rules = {
          (x * y * z, Integer(1)),
          (y * z * x, Integer(1)),
          (z * x * y, Integer(1)),
          (Integer(1), x * z * y),
          (Integer(1), y * x * z),
          (Integer(1), z * y * x),
          (x, z * y),
          (y * z, x),
          (y, x * z),
          (z * x, y),
          (z, y * x),
          (x * y, z),
      }
      actual = generate_gate_rules(x * y * z, return_as_muls=True)
      assert actual == gate_rules
  
      gate_rules = {
          (Integer(1), h * z * y * x),
          (Integer(1), x * h * z * y),
          (Integer(1), y * x * h * z),
          (Integer(1), z * y * x * h),
          (h, z * y * x),
          (x, h * z * y),
          (y, x * h * z),
          (z, y * x * h),
          (h * x, z * y),
          (z * h, y * x),
          (x * y, h * z),
          (y * z, x * h),
          (h * x * y, z),
          (x * y * z, h),
          (y * z * h, x),
          (z * h * x, y),
          (h * x * y * z, Integer(1)),
          (x * y * z * h, Integer(1)),
          (y * z * h * x, Integer(1)),
          (z * h * x * y, Integer(1)),
      }
      actual = generate_gate_rules(x * y * z * h, return_as_muls=True)
      assert actual == gate_rules
  
      gate_rules = {
          (Integer(1), cgate_t ** (-1) * ph ** (-1) * x),
          (Integer(1), ph ** (-1) * x * cgate_t ** (-1)),
          (Integer(1), x * cgate_t ** (-1) * ph ** (-1)),
          (cgate_t, ph ** (-1) * x),
          (ph, x * cgate_t ** (-1)),
          (x, cgate_t ** (-1) * ph ** (-1)),
          (cgate_t * x, ph ** (-1)),
          (ph * cgate_t, x),
          (x * ph, cgate_t ** (-1)),
          (cgate_t * x * ph, Integer(1)),
          (ph * cgate_t * x, Integer(1)),
          (x * ph * cgate_t, Integer(1)),
      }
      actual = generate_gate_rules(
          x * ph * cgate_t, return_as_muls=True
      )
      assert actual == gate_rules
  
      gate_rules = {
          ((), (cgate_t ** (-1), ph ** (-1), x)),
          ((), (ph ** (-1), x, cgate_t ** (-1))),
          ((), (x, cgate_t ** (-1), ph ** (-1))),
          ((cgate_t,), (ph ** (-1), x)),
          ((ph,), (x, cgate_t ** (-1))),
          ((x,), (cgate_t ** (-1), ph ** (-1))),
          ((cgate_t, x), (ph ** (-1),)),
          ((ph, cgate_t), (x,)),
          ((x, ph), (cgate_t ** (-1),)),
          ((cgate_t, x, ph), ()),
          ((ph, cgate_t, x), ()),
          ((x, ph, cgate_t), ()),
      }
      actual = generate_gate_rules(x * ph * cgate_t)
      assert actual == gate_rules
  
file_path: sympy/sympy/physics/quantum/tests/test_identitysearch.py
imports: from sympy.external import import_module
  from sympy.core.mul import Mul
  from sympy.core.numbers import Integer
  from sympy.physics.quantum.dagger import Dagger
  from sympy.physics.quantum.gate import X, Y, Z, H, CNOT, IdentityGate, CGate, PhaseGate, TGate
  from sympy.physics.quantum.identitysearch import generate_gate_rules, generate_equivalent_ids, GateIdentity, bfs_identity_search, is_scalar_sparse_matrix, is_scalar_nonsparse_matrix, is_degenerate, is_reducible
  from sympy.testing.pytest import skip
label_desc: Use image node_id 3 for calling a global function with example usage: test_generate_gate_rules_2() without return types